Expand `|(3,4),(2,5)|`

Answer

To expand the determinant \( |(3, 4), (2, 5)| \), we will follow these steps:

### Step 1: Set up the determinant
We start by defining the determinant as follows:
\[ \Delta = \begin{vmatrix} 3 & 4 \\ 2 & 5 \end{vmatrix} \]

### Step 2: Apply the formula for a 2x2 determinant
The formula for the determinant of a 2x2 matrix \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) is given by:
\[ ad - bc \]
In our case, \( a = 3 \), \( b = 4 \), \( c = 2 \), and \( d = 5 \).

### Step 3: Substitute the values into the formula
Now we substitute the values into the determinant formula:
\[ \Delta = (3 \cdot 5) - (2 \cdot 4) \]

### Step 4: Calculate the products
Now we calculate the products:
\[ 3 \cdot 5 = 15 \]
\[ 2 \cdot 4 = 8 \]

### Step 5: Subtract the second product from the first
Now we perform the subtraction:
\[ \Delta = 15 - 8 \]

### Step 6: Final result
Thus, we find:
\[ \Delta = 7 \]

### Summary of the solution
The value of the determinant \( |(3, 4), (2, 5)| \) is \( 7 \).

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